Perturbation theory in 3D potential

1. The problem statement, all variables and given/known data
Consider a quantum particle of mass m in a 3-D harnonic potential with frequency [itex]\omega[/itex] and it experiences a perturbation [itex]H_{1}=az^{2}[/itex]

a. Determine the effect of [tex]H_{1}[/tex] on the 1st exicted level of the system ( at the 1st order perturbation)

b. what happen to L[tex]^{2}[/tex] and [tex]L_{z}[/tex]? are they still conserved in presence of [tex]H_{1}[/tex]?

then find the value of <[itex]\Psi_{112}|az^{2}||\Psi_{112}[/itex]>, <[itex]\Psi_{121}|az^{2}||\Psi_{121}[/itex]>,
<[itex]\Psi_{211}|az^{2}||\Psi_{211}[/itex]>, susb [itex]z^{2}=r^{2}-x^{2}-y^{2}[/itex]
and [itex]x^{2}=\frac{\hbar}{2m\omega}[a^{2}_{+}+a_{+}a_{-}+a_{-}a_{+}+a^{2}_{-}][/itex]
but i don't know what is the representation for [itex]y^{2} and r^{2}[/itex]